There's a little truth to that, but a hell load of lies mixed in. This is the major case for manufacturers and sellers that want to push the products. I'll explain.
We've discussed in many extended details on why girth routines help with length, and length routines help with girth. But if you take an average data across the board for all devices, pumping for girth only helps to gain 10% of the length, and extenders use for length only helps to increase 10% of the girth. 10% is being very liberal on giving the devices the most optimal gains they can every hope to attain. Most gains are around 5% at best.
If that don't make sense, this will.
When you perform girth routines, especially in the pump, you are causing a pull on the tunica for length. You're engaging a tunica fiber weakening. Most people who only pump, nothing more but just pump (no SSJ, no prewarming stretches, nothing), do not see the length gain. The only reason why they gain some kind of length is because they are in a period of hyper growth. They have not stop growing, or they are in their period of high reproductive escapades. In other words, they're horny and they want to spread their semen. During this period, the body releases high level of human growth hormone and collagen to improve their reproductive chances. Their penises are easily influenced by abnormal changes. So, a little tug and pull on their penis may just be enough to trigger their body to release as much resources as possible to make their penises grow. When that happens, the companies want to use this phenomenon to say, "Our products will make your penis larger and longer!!" That only happens to those who are actually in the period of growth still. That means their age group is still young. Good luck in finding the same conditions apply to older age group.
The same is true for the length products, such as the extender. There's actually more truth to the extender than the pump. Why is that? When the extender is used to stretch the tunica, the tunica caused the surrounding tissues to also hyper extend and enlarged. Take a water hose for example. If you pump the hose up with higher pressure than the hose can handle, you only get lateral expansion. It gets larger before the hose bursts. BUT, if you stretch it slowly like an extender, The hose wall breaks down little by little and it stretches longer and longer. When your penis engages in erection from morning woods or through sexual excitement, like a stretched hose with thinner walls, the pressure influences an expansion more readily. In term the hose, the hose can both expand easier and doesn't explode like when the wall is more rigid. So, you have a longer hose and a larger expanding hose. Same for the penis. When the penis is extended in length, the surround tissues are also stretched to their limits. This allows any extra blood pressure to expand the cavernosa more readily, creating a "large" penis as well as a "longer" penis.
So, to compare side-by-side between pumping only and extender only for growth, pumping has up to 5% length growth influences, where as extender can push the limit to 10% girth growth influences. This has been recorded in growth data going back as far as 1980s.